Methods for monitoring thickness of a conductive layer

ABSTRACT

Methods and apparatuses for calibrating eddy current sensors. A calibration curve is formed relating thickness of a conductive layer in a magnetic field to a value measured by the eddy current sensors or a value derived from such measurement, such as argument of impedance. The calibration curve may be an analytic function having infinite number terms, such as trigonometric, hyperbolic, and logarithmic, or a continuous plurality of functions, such as lines. High accuracy allows the omission of optical sensors, and use of eddy current sensors for endpoint detection, transition call detection, and closed loop control in which a process parameter is changed based on the measured magnetic flux density change in one or more processing zones.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/105,060, filed Apr. 17, 2008, which is incorporated herein byreference in its entirety.

BACKGROUND

1. Field

The present application relates generally to layer thicknessmeasurement, and, more particularly, to layer thickness measurement inconductive layer processing tools.

2. Description of the Related Art

Integrated circuits are generally manufactured by forming variousmaterials, such as metals and dielectrics, on a wafer to createcomposite thin films and patterning the layers. It can often be usefulto have an accurate measure of the thickness of a layer formed on asubstrate. For example, a layer can be initially over-deposited onto thewafer to form a relatively thick layer, and a planarization process isemployed to thin the layer to a desired thickness. Knowing the thicknessof the layer can help control the planarization process.

Methods of determining layer thickness include in situ and ex situtechniques. Known processes each have particular advantages anddisadvantages for various applications.

SUMMARY

In certain embodiments, a method of processing a wafer compriseschanging the thickness of a conductive layer on the wafer and duringchanging, monitoring the thickness of the conductive layer. Monitoringthe thickness comprises correlating a measurement from an eddy currentsensor to a thickness of the conductive layer. Correlating themeasurement to the thickness comprises applying a model that includeseither (1) a plurality of functions between measurement points of knownthicknesses or (2) an analytic function having infinite order terms.

In certain embodiments, a method of determining a thickness of aconductive layer on a workpiece comprises measuring a magnetic fluxdensity change when the conductive layer on the workpiece is in amagnetic field and calculating the thickness of the conductive layerusing a calibration curve formed by relating the magnetic flux densitychange to thickness of a conductive layer disposed in the magneticfield. The calibration curve either fits a smooth function interpolationto a plurality of calibration points or connects the plurality ofcalibration points with a plurality of functions.

In certain embodiments, a method of calibrating an eddy current sensorcomprises generating a magnetic field, measuring an argument ofimpedance when each of a plurality of wafers comprising conductivelayers having known thicknesses are passed therethrough, forming acalibration curve fitting the measured arguments of impedance to theknown thicknesses. The calibration curve comprises either an analyticfunction having infinite order terms or a continuous piecewise function.

In certain embodiments, a method of determining a thickness of aconductive layer on a workpiece comprises using an eddy current sensorto measure a value when the conductive layer on the workpiece is in amagnetic field and calculating the thickness of the conductive layerusing a calibration curve that correlates thickness to the measuredvalue. The calculated thickness is within 5% error over a range fromabout 1 kÅ to about 20 kÅ.

In certain embodiments, an apparatus for determining thickness comprisesan eddy current sensor calibrated to measure a magnetic flux densitychange when a conductive layer on a workpiece is in a magnetic field anda processor configured to execute a program that transforms the measuredmagnetic flux density change into a calculated thickness of theconductive layer. The program comprises a calibration curve fit to aplurality of calibration points. The calibration curve comprises eithera smooth function interpolation or a piecewise function.

For purposes of summarizing the invention and the advantages achievedover the prior art, certain objects and advantages of the invention aredescribed herein. Of course, it is to be understood that not necessarilyall such objects or advantages may be achieved in accordance with anyparticular embodiment of the invention. Thus, for example, those skilledin the art will recognize that the invention may be embodied or carriedout in a manner that achieves or optimizes one advantage or group ofadvantages as taught or suggested herein without necessarily achievingother objects or advantages as may be taught or suggested herein.

All of these embodiments are intended to be within the scope of theinvention herein disclosed. These and other embodiments will becomereadily apparent to those skilled in the art from the following detaileddescription of the preferred embodiments having reference to theattached figures, the invention not being limited to any particularembodiment(s) disclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the inventiondisclosed herein are described below with reference to the drawings ofpreferred embodiments, which are intended to illustrate and not to limitthe invention.

FIG. 1 is a schematic plan view of an example embodiment of an orbitalchemical mechanical polishing tool.

FIG. 2A is a cross sectional side view of an example embodiment of apolishing station that may be implemented into the tool of FIG. 1.

FIG. 2B is a cross sectional side view of another example embodiment ofa polishing station that may be implemented into the tool of FIG. 1.

FIG. 3A is a schematic plan view of a wafer, polishing pad, and eddycurrent sensors for use in a polishing station of the type shown in FIG.2A.

FIG. 3B is a schematic plan view of a wafer, polishing pad, and eddycurrent sensors for use in a polishing station of the type shown in FIG.2B.

FIG. 4 is an example plot of calculated thickness versus the modulus ofimpedance.

FIG. 5 is an example plot of calculated thickness versus argument ofimpedance θ.

FIGS. 6A-6E are example plots of modeled thicknesses and actualthicknesses versus argument of impedance θ using various orders ofpolynomials for modeling.

FIG. 7 is an example plot of actual thickness and a modeled thicknessfunction versus argument of impedance θ.

FIG. 8 is an example plot of thickness measurement error using a modeledthickness function.

FIG. 9 graphically depicts linear piecewise continuous interpolation.

FIG. 10A is an example plot of actual thickness and modeled thicknessesfor linear piecewise continuous interpolation versus argument ofimpedance θ.

FIGS. 10B and 10C are example plots of actual thickness and modeledthicknesses for polynomial piecewise continuous interpolations versusargument of impedance θ.

FIG. 11 is an example plot of thickness measurement error using aplurality of modeled thickness functions.

FIGS. 12A and 12B are example plots of endpoint call times using avariety of techniques.

FIG. 13A is an example plot of conductive layer thickness during removalprior to a transition detection.

FIG. 13B is an example plot of conductive layer thickness remainingafter a transition detection.

FIG. 14 is an example conductive layer thickness profile before andafter polishing using a variety of techniques.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

A chemical mechanical polishing (“CMP”) process can thin a layer on asemiconductor substrate, such as a wafer, and remove projections andimperfections by contacting the layer with a polishing surface (e.g., apad) and a slurry, which typically contains abrasive particles. Relativemotion between the wafer and the polishing surface is provided at aselected rate, pressure, temperature, etc., which may be controlled toyield a layer having a desired thickness. While embodiments may bedescribed with respect to certain CMP tools and process techniques, theskilled artisan will appreciate that the measurement techniquesdisclosed herein have applications to stand alone or ex situ measurementstations or other types of processing tools.

FIG. 1 illustrates a CMP apparatus 20 that combines a plurality of CMPsystems 22 in a work efficient and space efficient manner. Preferably,the CMP systems 22 are arrayed in two rows spaced apart by a serviceaccess corridor 98. The CMP apparatus 20 includes a front end module 24that includes a cleaning module 76 having a plurality of cleaningstations 26 arrayed along a line at the end of, and substantiallyperpendicular to, the rows of CMP systems 22. In such a CMP apparatus20, a plurality of semiconductor wafers can be polished in parallel inthe CMP systems 22, and then can be cleaned in parallel in the cleaningstations 26. Although four CMP systems 22 and three cleaning stations 26are illustrated, the CMP apparatus 20 can include a greater or lessernumber of either.

The front end module is further configured to include a wafer cachestation 28 that can accommodate a plurality of individual wafer caches30, such as a cassette or front opening unified pod (FOUP) receiver. Thecassette/FOUP receiver 30 is configured to receive cassettes/FOUPShousing one or more workpieces. A front end or “dry” robot 32(configured to handle dry workpieces) is located in the front end moduleand employed to transfer a selected wafer from a selected wafer cache 30to a wafer hand off station 34. A transfer or “wet” robot 36 (configuredto handle wet workpieces), positioned between the two rows of CMPsystems 22, retrieves the selected wafer from the hand off station andtransfers it to a selected one of the plurality of CMP systems 22. Insome embodiments, the transfer robot 36 includes a transfer load cup(TLC) configured to transport the workpiece or substrate among thepolishing stations CMP systems 22. In certain embodiments, each CMPsystem 22 is configured to operate independently from the others and maybe configured to perform specific functions of the CMP process, such as,but not limited to, having separate stations for sequentialnon-selective (fast) copper removal, (slower) selective copper removal,and barrier layer removal. In certain alternative embodiments, two ormore of the CMP systems 22 are configured to operate together, forexample to sequentially operate on some workpieces.

A slurry container (not shown) may be externally or internallyassociated to supply CMP slurry to the CMP systems 22 through at leastone supply channel (not shown). Multiple different CMP slurries may beused. CMP slurries may be supplied to a workpiece via any one ofnumerous conventionally used methods. For example, a CMP slurry can besupplied to a polishing platen for a through-the-pad polishing system.For another example, CMP slurry can be supplied to a workpiece holderfor systems in which the slurry is dispensed onto the workpiece surface.In a third example, CMP slurry can be supplied onto the top surface ofthe polishing pad from a dispenser located on the system 104. In someembodiments, the CMP slurry comprises an electrolyte that can be platedonto the workpiece.

The selected wafer is polished at the selected CMP system 22. Uponcompletion of the polishing operation, the wafer is transferred by thetransfer robot 36 from the selected CMP system 22 to another of the CMPsystems 22 for further processing, or is transferred to a selected oneof the plurality of cleaning stations 26 for cleaning. When the cleaningoperation is completed, the front end robot 32 transfers the nowplanarized and cleaned wafer to one of the wafer caches 30. As usedherein, the terms “unprocessed wafer” or “unprocessed workpiece” shallrefer to a wafer or workpiece prior to a CMP operation, and the terms“processed wafer” or “processed work piece” shall refer to a wafer orworkpiece after a CMP operation. In certain embodiments, the CMPapparatus 20 includes at least one controller 130 that is incommunication with the CMP systems 22 and/or the cleaning stations 26and that is configured to operate the CMP systems 22 and/or the cleaningstations 26.

FIG. 2A illustrates a cross sectional side view of an example embodimentof a polishing station 200 that may be incorporated into the CMPapparatus 20 as any one or all of the CMP systems 22. The polishingstation 200 is configured to polish a workpiece 202, which may includean exposed conductive layer 205 and other layers (not shown). Thepolishing station 200 includes a lower polishing module 204 and aworkpiece carrier 206. The lower polishing module 204 includes a platen208 and a polishing pad 210. The platen 208 may comprise a plurality ofstacked manifold layers. The platen 208 can optionally be configured toserve several purposes, including introducing relative motion betweenthe polishing pad 210 and the workpiece 202. In this regard, the platen208 is coupled to a motor assembly 228 that is configured to move theplaten 208 orbitally. Other systems may be configured to move a platenin various directions (e.g., translationally, orbitally, and/orrotationally). The platen 208 may be configured to provide conduits fordelivering polishing slurry or other fluids to the top surface of thepolishing pad 210 and/or other devices. For example, as depicted in FIG.2A, the platen 208 includes openings 212 a, 212 b through whichpolishing fluid may be dispensed to the polishing surface of the pad210, although it will be appreciated that polishing fluid may bedelivered over the polishing pad 210, through conduits on the tool orthe wafer carrier assembly 206, etc.

As mentioned above, the polishing pad 210 is configured to polish theworkpiece 202 when the workpiece 202 is urged against the pad 210. Thepolishing pad 210 may be any type of device conventionally used forpolishing workpieces 202, for example a polyurethane polishing padavailable from Rohm and Haas of Philadelphia, Pa. The polishing pad 210has a predetermined initial thickness and is removably coupled to platen208 such that the polishing pad 210 may be used for a plurality ofpolishing operations and replaced once the thickness is determined to nolonger be satisfactory. In some embodiments, the polishing pad 210includes a sub-pad.

The workpiece carrier 206 is configured to receive a workpiece 202 andto urge the workpiece 202 against the polishing pad 210 during apolishing process. The carrier 206 applies a vacuum-like force to theback side of the workpiece 202, retains the workpiece 202, moves towardthe polishing pad 210 to place the workpiece 202 in contact with thepolishing pad 210, releases the vacuum-like force, and then applies aforce to the workpiece 202 toward the polishing pad 210. In certainembodiments, the carrier 206 is configured to cause the workpiece 202 tomove (e.g., rotationally, orbitally, translationally). The carrier 206includes a body 220, a retaining ring 232 configured to retain theworkpiece 202 during polishing, a bladder or diaphragm 218, and a meansfor applying pressure to the bladder 218.

The carrier 206 illustrated in FIG. 2A has three concentric zones: acentral zone 215, an intermediate zone 216, and a peripheral zone 217.The bladder 218 provides a surface for supporting the workpiece 202. Aninner ring 210 provides a barrier for separating the zones 215, 216 andan outer ring 211 provides a barrier for separating the zones 216, 217.While three zones 215, 216, 217 are illustrated in FIG. 2A, any suitablenumber of zones may be used. The greater the number of zones, the morecontrol over the planarization of the workpiece surface 205 may beexercised. In the workpiece carrier 206 illustrated in FIG. 2A, themeans for applying pressure to the bladder 218 is adapted to permitbiasing the pressure exerted on different areas of the back surface ofthe wafer 202 by the zones 215, 216, 217. Areas on the back surface ofthe workpiece 202 receiving a higher (or lower) pressure will typicallyincrease (or decrease) the removal rate of material from correspondingareas on the front surface 205 of the workpiece 202. Removal rates ofmaterial from planarization processes are typically substantiallyuniform within concentric annular bands about the center of theworkpiece 202, but the carrier 206 is preferably capable of exertingdifferent pressures in a plurality of different areas while maintaininga uniform pressure within each area. In addition, the carrier 206 alsois able to apply different pressures over different zones 215, 216, 217on the back surface of the workpiece 202. The pressure within thecentral 215, intermediate 216, and peripheral 217 zones may beindividually communicated through passageways 235, 236, 237,respectively, by controllable pressure regulators 245, 246, 247,respectively, each connected to a pump 226. A rotary union 220 may beused to communicate pressure from the pump 226 to each of the pressureregulators 245, 246, 247, and thus to their respective zones 215, 216,217 if the carrier 206 is rotated. Thus, each concentric zone 215, 216,217 may be individually pressurized to create three concentric bands topress against the back surface of the workpiece 202. Each zone 215, 216,217 may therefore have a different pressure, but each concentric bandwill therefore have a uniform pressure within the band to press againstthe back surface of the workpiece 202.

The bladder 218 provides a vacuum-like force when the carrier 206 iscontacted to the workpiece 202 to retain the workpiece 202, and isconfigured to provide a controlled pressure across a backside of theworkpiece 202 during a polishing process. In certain embodiments, thebladder 218 comprises a plurality of independently controllable zones.Each zone may be connected to an independent supply of fluid used topressurize the zones and to apply pressure to the back of the workpiece202.

In certain embodiments, the CMP apparatus 20 includes a set ofelectrodes (not shown) configured to electrochemically plate or polishthe conductive layer 205 of the workpiece 202, for example as describedin co-owned U.S. Pat. No. 6,497,800. When the CMP apparatus (e.g.,FIG. 1) is used for electrochemical plating, a first electrode rendersthe workpiece 202 cathodic with respect to a second electrode such thatmolecules of metal in an electrolyte solution are deposited on thesurface of the workpiece 202. During plating, the polishing pad 210 maybe used to polish the deposited conductive material. When the CMPapparatus 20 is used for electrochemical polishing, a first electroderenders the workpiece 202 anodic with respect to a second electrode suchthat molecules of metal are etched from the surface of the workpiece 202in an electrolyte solution. During polishing, the polishing pad 210 maybe used to planarize the conductive material during removal.

The platen 208 also includes an eddy current probe or sensor 214. Theeddy current probe 214 generates a magnetic field that experiences achange in magnetic flux density when a conductive object (e.g., theconductive metal layer 205 on a workpiece 202) is passed therethrough.The magnetic flux change provides measurements that can be plotted on animpedance plane. The data points of the impedance plane are typicallyrepresented as (x,y) coordinates, as described by Equation 1:z=x+i·y  Eq. 1where x is the real part from the dry resistance and y is the imaginarypart influenced by the reactance of the layer, which is a combination ofinductance and capacitance. The measurements can be used to determinecertain parameters, such as the hardness or density of the workpiece202, the thickness of the conductive layer 205, and to identify defectsin the conductive layer 205.

The eddy current probe 214 may be disposed in any suitable portion ofpolishing station 200. In some embodiments, the eddy current probe 214is disposed in an opening 212 c in the platen 208, as illustrated inFIG. 2A. In certain alternative embodiments, the eddy current probe 214is disposed adjacent and proximate to the platen 208. Additionally,although a single eddy current probe 214 is depicted in FIG. 2A, it willbe appreciated that a plurality of eddy current probes 214 may bedisposed in a plurality of positions to measure different zones of theworkpiece 202. The probes 214 may be mounted in a variety of positionswith respect to the pad 210 (e.g., flush with the pad, under the pad,under a sub-pad, etc.).

FIG. 2B illustrates a cross sectional side view of another exampleembodiment of a polishing station 250 that may be incorporated into theCMP apparatus 20 as any one or all of the CMP systems 22. The polishingstation 250 is configured to polish a workpiece 202, which may includean exposed conductive layer 205 and other layers (not shown). Thepolishing station 250 includes a lower polishing module 254 and aworkpiece carrier 206, for example as described above with respect toFIG. 2A. The lower polishing module 254 includes a platen 258 and apolishing pad 260. The platen 258 can optionally be configured to serveseveral purposes, including introducing relative motion between thepolishing pad 260 and the workpiece 202. In this regard, the platen 258is coupled to a motor assembly 228 that is configured to rotate theplaten 258. In certain embodiments, the pad 260 and platen 258supporting the pad 260 are at least twice the diameter of the workpiece202. In certain modes of operation, the platen 258 rotates about theaxis 264, and the carrier 206 rotates about the axis 266 such that theworkpiece 202 traces a circular path around the pad 260. The platen 258may be configured to provide conduits for delivering polishing slurry orother fluids to the top surface of the polishing pad 260 and/or otherdevices. For example, as depicted in FIG. 2B, the platen 258 includesopenings 212 a, 212 b through which polishing fluid may be dispensed tothe polishing surface of the pad 260. For another example, a slurrydispenser 262 may be disposed above the pad 260. Other fluid deliverysystems are also possible.

FIG. 3A illustrates a top plan view of an embodiment of a polishingstation 200 in which a workpiece 202 is disposed on a polishing pad 210.A plurality of eddy current sensors 300 a, 300 b, 300 c, 300 d arepositioned below, and generally in fixed relation to, the polishing pad210 (e.g., within the platen 208 of FIG. 2A). As the workpiece 202 andthe polishing pad 210 are moved relative to each other, the sensors 300a, 300 b, 300 c, 300 d are able to detect a change in magnetic fluxdensity at different positions on the workpiece 202. For example, in theoriginal position of the workpiece 202, represented by a solid line, thesensor 300 a at the periphery of the pad 210 does not produce a readingof the workpiece 202, but if the workpiece 202 is moved to the positionof the dashed line, the sensor 300 a produces a reading based on thethickness of the conductive layer 205 at the edge of the workpiece 202.

FIG. 3B illustrates a top plan view of another embodiment of a polishingstation 200 in which a workpiece 202 is disposed on a polishing pad 260.A plurality of eddy current sensors 300 a, 300 b, 300 c, are positionedbelow, and generally in fixed relation to, the polishing pad 260 (e.g.,within the platen 258 of FIG. 2B). As the workpiece 202 and thepolishing pad 260 are moved relative to each other, the sensors 300 a,300 b, 300 c, are able to detect a change in magnetic flux density atdifferent positions on the workpiece 202. For example, in the originalposition of the workpiece 202, represented by a solid line, none of thesensors 300 a, 300 b, 300 c produce a reading of the workpiece 202, butif the workpiece 202 is moved to the position of the dashed line, all ofthe sensors 300 a, 300 b, 300 c produce a reading based on the thicknessof the conductive layer 205. Depending on the speed of rotation of thelower polishing module 254, the sensors 300 a, 300 b, 300 c may only bebeneath the workpiece 202 for a fraction of the polishing time. Incertain such systems, data from the sensors 300 a, 300 b, 300 c may besparse compared to the embodiment illustrated in FIG. 3B (in which threesensors can continuously produce data), although appropriate samplingrates may still be used to determine thickness of the conductive layer205 of the workpiece 202.

In order to correlate a single value for the two impedance coordinates,the variables x, y provided by an eddy current sensor to a thickness ofa conductive layer, the modulus of impedance, as described by Equation2, may be used.|z|=√{square root over (x ² +y ²)}  Eq. 2Accordingly, a single value for a modulus of impedance |z| may becalculated for a given conductive layer thickness. However, a singlethickness may not always be calculable for a given modulus of impedance|z| because the thickness is not a monotonic function of the modulus ofimpedance |z| over a broad thickness range, nor is the thickness amonotonic function of the natural log of the modulus of impedance ln|z|(i.e., for any given modulus |z|, there may be two or more correspondingpossible thicknesses).

FIG. 4 is an example plot of calculated thickness versus modulus ofimpedance |z| for four eddy current probes (e.g., the probes 300 a, 300b, 300 c, 300 d). Each of the plots has portions in which a plurality ofthicknesses can be calculated from a single measurement of modulus ofimpedance |z| due to the non-monotonic nature of the correlation. Assuch, calculating a thickness based on a measurement of modulus ofimpedance |z| can be challenging or impossible. For example, a modulusof impedance |z| of about 1650 as measured by Probe 4 could result in athickness of about 14.5 kÅ or a thickness of about 20 kÅ, a differenceof about 38%. Accordingly, the modulus of impedance |z| generally cannotbe used to provide accurate thickness data, especially over a largerange of thicknesses.

The thickness is also not a monotonic function of either the dryresistance x or the reactance y, and thus using only one of thevariables may have similar accuracy issues. However, the disclosurebelow takes advantage of the realization that thickness is a monotonicfunction of the argument of z (i.e., the phase angle θ represented inEquation 3), and therefore can be used to correlate impedance values xand y measured by an eddy sensor to a unique thickness value.

$\begin{matrix}{\theta = {\tan^{- 1}\left( \frac{y_{b}}{x_{b}} \right)}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$where the subscript b indicates that the raw data has been corrected forthe zero-error, commonly called the “balanced data” after balancing thesensors as follows:z=Re ^(iθ)z _(raw) =x _(raw) +y _(raw)z ₀ =x ₀ +i·y ₀z _(b) =x _(b) +i·y _(b)=(x _(raw) −x ₀)+i·(y _(raw) −y ₀)where z₀ is the impedance measured without any calibration wafer frompoints x₀ and y₀, which are subtracted from the measured impedancevalues x_(raw) and y_(raw) to result in the balanced impedance valuesx_(b) and y_(b). The argument of impedance θ can then be accuratelycalculated by determining the arctangent of the ratio of the balancedvalues y_(b) to x_(b). Calibration using two or more points and linearor polynomial curve fitting can correlate the measured impedance toknown or measured thicknesses.

FIG. 5 is an example plot of calculated thickness versus “measured”argument of impedance θ, calculated from the impedance measured by foureddy current probes (e.g., the probes 300 a, 300 b, 300 c, 300 d). Allof the probe measurements show monotonic variation of the argument ofimpedance θ with thickness over a large range of thickness values. Thus,a one-to-one mapping between thickness and the argument of impedance θcan be established. The mapping can be used to calibrate the sensors,thereby enabling the sensors to work over a large range of thicknesses.

Eddy current measurements can be correlated to measured or knownthicknesses based on the phase angle or argument θ, but a mathematicalrelation between the calibration measurements is needed forinterpolation or extrapolation. For typical engineering calibrations,the most commonly used curve fits to the data are linear and polynomialcurve fits. However, they cannot be used reliably for fitting themodulus of impedance over large thickness ranges because there may be alarge amount of error between the calibration points, particularly atlow and high thicknesses. The correlation may be tightened by usinghigher order polynomials (e.g., up to the fifth power), but higher orderpolynomials also induce higher error as a result of fitting each of thecalibration points. In certain systems, the amount of error isacceptable for layers having a relatively small thickness range (e.g.,between about 1 kÅ and about 10 kÅ), but the error can be about 15% ormore when the thickness range is expanded (e.g., to less than about 500Å and greater than about 20 kÅ) due to poor fit by the calibrationcurve.

The poor correlation of polynomial calibration curves fit to known orotherwise measured thickness data points is illustrated in FIGS. 6A-6E.FIG. 6A illustrates a second order polynomial calibration curve fit to aset of calibration data, which is represented by the circles. The curvedoes not fit the data points well at most thicknesses and the error atlow thicknesses (e.g., at about 4 kÅ) is extreme. The calculatedthickness using the curve to interpolate or extrapolate is only accuratewithin about 22%, even at the data points representing actually measuredthicknesses, and is worst at low thicknesses (i.e., below about 5 kÅ),where the calculated thickness value should desirably be most accurate.FIG. 6B illustrates a third order polynomial calibration curve fit tothe same set of calibration data, represented by the circles. Thecalculated thickness using the curve to interpolate or extrapolate isonly accurate within about 9%, even at the actually measuredthicknesses, and is again worst at low thicknesses (i.e., below about 5kÅ), where the calculated thickness value should desirably be mostaccurate. FIG. 6C illustrates a fourth order polynomial calibrationcurve fit to the same set of calibration data, represented by thecircles. The calculated thickness using the curve to interpolate orextrapolate is accurate within about 4% at the actually measuredthicknesses, but can be inaccurate by more than 9% at some lowthicknesses (i.e., below about 5 kÅ), where the calculated thicknessvalue should desirably be most accurate. FIG. 6D illustrates a fourthorder polynomial calibration curve fit to the same set of calibrationdata, represented by the circles. The calculated thickness using thecurve to interpolate or extrapolate is accurate for the calibrationpoints, but begins to vary wildly from the actual data at lowthicknesses (i.e., below about 5 kÅ), where the calculated thicknessvalue should desirably be most accurate. FIG. 6E illustrates a fifthorder polynomial calibration curve fit to the same set of calibrationdata, represented by the circles. The calculated thickness using thecurve to interpolate or extrapolate is accurate for the calibrationpoints, but begins to vary even more wildly from the actual data at lowthicknesses (i.e., below about 5 kÅ), where the calculated thicknessvalue should desirably be most accurate, even predicting negativethickness values at some phase angle (argument of impedance)measurements. Thus, lower order polynomials fail to fit even calibrationdata, and higher order polynomials fail to accurately fit thecalibration data to a reasonable curve. Accordingly, polynomials ingeneral, and higher order polynomials in particular, are not thesolution to producing calibration curves that correctly model thicknessbased on eddy current measurements.

Additionally, the order of the polynomial is disadvantageously limitedby the number of calibration wafers used (i.e., at least fourcalibration wafers and a non-wafer—or zero—reading are needed to obtaina predictive fifth-order polynomial). Increasing the number ofcalibration wafers will enable a fit of the calibration curve to ahigher number of points, but it becomes more time consuming, therebydecreasing the amount of time the CMP apparatus 20 may use to processproduction workpieces. Moreover, a combination of high quantities ofcalibration wafers and a high order polynomial can actually producelarge error as the polynomial will fit each calibration point but bewildly inaccurate for interpolations or extrapolations that are not nearthose actual data points, as illustrated in FIG. 6E.

Smooth Function Interpolation

The present disclosure takes advantage of the realization thatminimization of the distance between calibration points and thecalibration curve fit can produce less error for interpolations orextrapolations distant from the actual data points used to generate thecalibration curve. An appropriate system of functions is expressed byEquations 4-6:

$\begin{matrix}{t = {\sum\limits_{j}\;{g_{j}\left( {a_{j},\theta} \right)}}} & {{Eq}.\mspace{14mu} 4} \\{{g_{j} \cdot \left( {a_{j},\theta} \right)} = {a_{j} \cdot {h_{j}(\theta)}}} & {{Eq}.\mspace{14mu} 5} \\{{h_{j}(\theta)} = \left\{ \begin{matrix}\theta^{j - 1} \\{\sin\left( {{\overset{\_}{\omega}}_{j},\theta} \right)} \\{\sinh\left( {j \cdot \theta} \right)}\end{matrix} \right.} & {{Eq}.\mspace{14mu} 6}\end{matrix}$where t is thickness, where j is an index variable holding the place ofthe number of terms, where g_(j)·(a_(j),θ) is any function in which theconstants a_(j) can be separated from the function h_(j)(θ), and wherethe function h_(j)(θ) could be any type of analytic function havinginfinite order terms (e.g., trigonometric, hyperbolic, logarithmic,inverse trigonometric, inverse hyperbolic, inverse logarithmic,combinations thereof, and the like, as expressed in the examples ofEquation 6). This excludes purely polynomial functions, which havefinite order terms (i.e., the number of terms based on the order of thepolynomial). In certain embodiments, the function h_(j)(θ) could includea polynomial in combination with an analytic function having infiniteorder terms (e.g., hyperbolic in combination with a fourth-orderpolynomial). Embodiments in which the function is hyperbolic sine,(e.g., h_(j)(θ)=sin h(j·θ)), generally can provide good curve fit toeddy current calibration data (e.g., thickness versus argument ofimpedance θ) because such a function is infinitely differentiable andcan thereby accurately capture decay and/or growth.

Once the function h_(j)(θ) has been selected for Equation 6, the valuesof the constants a_(j) may be calculated. For known thicknesses t_(i) ofi number of wafers, an eddy current sensor can be used to measure thearguments of impedance θ_(i) for the known thickness t_(i) on each waferi. Moreover, for known arguments of impedance θ_(i) and estimates ofeach value of a_(j), a reference thickness t_(i) ^(r) can be calculatedfor each wafer i, as expressed by Equation 7:

$\begin{matrix}{t_{i}^{r} = {\sum\limits_{j}\;{g_{j}\left( {a_{j},\theta_{i}} \right)}}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$The difference between the calculated reference thickness t_(i) ^(r) andthe actual thickness t_(i) is the error due to using improper values forthe constants a_(j), which is expressed in Equation 8:d _(i) =t _(i) −t _(i) ^(r)  Eq. 8The sum of the squares of the error in calculated reference thicknesst_(i) ^(r) for each wafer i is expressed by D² in Equation 9:

$\begin{matrix}{D^{2} = {{\sum\limits_{i}\; d_{i}^{2}} = {\sum\limits_{i}\;\left\lbrack {t_{i} - \left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)} \right\rbrack^{2}}}} & {{Eq}.\mspace{14mu} 9}\end{matrix}$The error can be minimized by taking a partial derivative of q terms.When the index j is the same as the index q, the partial derivative iszero, as expressed in Equation 10:

$\begin{matrix}{\frac{\partial D^{2}}{\partial a_{q}} = 0} & {{Eq}.\mspace{14mu} 10}\end{matrix}$When the index j is different than the index q, the partial derivativeis not zero and is used to populate a matrix.

$\begin{matrix}{\frac{\partial D^{2}}{\partial a_{q}} = {\frac{\partial}{\partial a_{q}}\left\{ {\sum\limits_{i}\;\left\lbrack {t_{i} - \left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)} \right\rbrack^{2}} \right\}}} \\{= {\frac{\partial}{\partial a_{q}}\left\{ {\sum\limits_{i}\;\left\lbrack {t_{i}^{2} - {2\;{t_{i}\left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)}} + \left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)^{2}} \right\rbrack} \right\}}} \\{= {{\frac{\partial}{\partial a_{q}}\left\lbrack {\sum\limits_{i}\;{{- 2}\;{t_{i}\left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)}}} \right\rbrack} + {\frac{\partial}{\partial a_{q}}\left\lbrack {\sum\limits_{i}\;\left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)^{2}} \right\rbrack}}} \\{= {{\sum\limits_{i}\;{{- 2}\; t_{i}\frac{\partial}{\partial a_{q}}\left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)}} + {\sum\limits_{i}\;{2\left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)}}}} \\{\frac{\partial}{\partial a_{q}}\left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)\frac{\partial}{\partial a_{q}}\left( {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right)} \\{= {\sum\limits_{j}\;\left( {\frac{\partial a_{j}}{\partial a_{q}} \cdot {h_{j}\left( \theta_{i} \right)}} \right)}} \\{= {\sum\limits_{j}\;{\delta_{jq} \cdot {h_{j}\left( \theta_{i} \right)}}}} \\{= {h_{q}\left( \theta_{i} \right)}}\end{matrix}$Equation 10 can thus be reduced to:

$\frac{\partial D^{2}}{\partial a_{q}} = {\sum\limits_{i}\;\left\lbrack {{{- 2}\;{t_{i} \cdot {h_{q}\left( \theta_{i} \right)}}} + {2{\left( {\sum\limits_{i}\;{a_{j} \cdot {h_{j}\left( \theta_{i} \right)}}} \right) \cdot {h_{q}\left( \theta_{i} \right)}}}} \right\rbrack}$

The system of Equations 4-10 results in Equations 11-14:[A]{a}={b}  Eq 11where [A] is a column matrix, where {a} is a square matrix of theconstants a_(j), and where {b} is a square matrix. Each term in thecolumn matrix [A] may be expressed as:

$\begin{matrix}{A_{qj} = {\sum\limits_{i}\;{{h_{q}\left( \theta_{i} \right)} \cdot {h_{j}\left( \theta_{i} \right)}}}} & {{Eq}.\mspace{14mu} 12}\end{matrix}$The thickness t_(i) is known for each a_(j)·h_(j)(θ_(i)), so each termb_(q) in the square matrix {b} may be expressed as:

$\begin{matrix}{b_{q} = {\sum\limits_{i}\;{{h_{q}\left( \theta_{i} \right)} \cdot t_{i}}}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

The result is Equation 14, which is devoid of the index i:A _(qj) ·a _(k) =b _(q)  Eq. 14Advantageously, this allows any number i of calibration wafers to beused for functions h_(j)(θ) having any number of terms. While morecalibration wafers can produce a more accurate function, about five (5)wafers (plus a non-wafer (e.g., “zero”) measurement) have been found tobe sufficient to determine thicknesses within 5% error over a largerange of conductive layer thicknesses when h_(j)(θ)=sin h(j·θ). Incertain embodiments, calibration can be performed using less than 20wafers, less than 10 wafers, less than 8 wafers, less than 6 wafers,less then 4 wafers, etc.

If the formed matrix is poorly scaled, Equation 15 can be used toprecondition the matrix for scaling and normalization.

$\begin{matrix}\begin{matrix}{t = {\sum\limits_{j}\;{a_{j} \cdot {h_{j}(\theta)}}}} \\{= {\sum\limits_{j}\;{a_{j} \cdot {h_{j}\left( \overset{\_}{\theta} \right)} \cdot \left( \frac{h_{j}(\theta)}{h_{j}\left( \overset{\_}{\theta} \right)} \right)}}} \\{= {\sum\limits_{j}\;{{\overset{\sim}{a}}_{j} \cdot \left( \frac{h_{j}(\theta)}{h_{j}\left( \overset{\_}{\theta} \right)} \right)}}}\end{matrix} & {{Eq}.\mspace{14mu} 15}\end{matrix}$where θ is the average of the measured arguments of impedance θ_(i), asexpressed by Equation 16, and where ã_(j)=a_(j)·h_(j)( θ):

$\begin{matrix}{\overset{\_}{\theta} = \frac{\sum\limits_{i}\;\theta_{i}}{i_{\max}}} & {{Eq}.\mspace{14mu} 16}\end{matrix}$

However, it will be appreciated that the calculated value of h_(j)( θ)should not be zero or else the normalization would disadvantageously bedividing by zero, leading to an undetermined result. Preconditioning thematrix using an average θ of the measured arguments of impedance θ_(i)can make the model more robust to large thickness ranges because itallows scaling of terms that would otherwise diverge.

Those of skill in the art will appreciate that methods described hereinmay be incorporated into computer code (e.g., into MATLAB® code) toautomate determination of the coefficients a_(j) of the functiong_(j)(a_(j),θ). Referring again to FIG. 2, the eddy current sensor 214may be in communication with the at least one controller 130, which mayinclude a processor configured to execute a program that transforms aparameter measured by the eddy current sensor 214 (e.g., change inmagnetic flux density, argument of impedance θ) into a thickness of theconductive layer 205 in accordance with the smooth functioninterpolation methods described herein.

FIG. 7 illustrates how the function h_(j)(θ)=sin h(j·θ) calibrationcurve compares to the same calibration data used for FIGS. 6A-6E, againrepresented by the circles. The calculated thickness using the argumentof impedance θ is correlated within about 2% at the actually measuredthicknesses, and is also accurate to within about 2% at intermediate(interpolated) thicknesses, including low amounts of error at low andhigh thicknesses (i.e., at about 1.8 kÅ and at about 20 kÅ), where thecalculated thickness value should desirably be most accurate. In certainembodiments, the calibration is advantageously stable at about zerothickness. In certain such embodiments, accuracy at about zero thicknessmay be improved by using an impedance measurement measured on a knownthickness of zero (e.g., no calibration wafer or a calibration waferfree of a conductive layer) in the calibration.

FIG. 8 illustrates the amount of conductive layer thickness measurementerror using a plurality of eddy current probes calibrated with ahyperbolic analytic function on wafers having known thicknesses fromabout 1.8 kÅ to about 21 kÅ. Certain probes may have different amountsof error based on their location on the workpiece 202 (e.g., the firstprobe or sensor 300 a may have more error than the second probe orsensor 300 b because the sensor 300 a may be off the workpiece 202 ormeasuring only the edge, while the sensor 300 b generally measures acentral region of the workpiece 202) or due to inherent probedifferences. In accordance with the method discussed above, the eddycurrent measurements were translated into arguments of impedance θ foreach calibration wafer, the data was normalized using an average value θof the arguments of impedance θ_(i), and a matrix was assembled todetermine the constants a_(j). The arguments of impedance θ were thenmeasured for a plurality of wafers using the same eddy current sensors,and the actual thickness was compared to the calculated thickness. Theerror for thicknesses calculated from sin h(j·θ) as determined by eddycurrent calibration measurements from all probes at all thicknesseswithin the measured range was less than about 5%, with a maximumstandard deviation of 1.7% on the worst performing probe (Probe 1).

Piecewise Continuous Interpolation

As described above, embodiments take advantage of the realization thatminimization of the distance between calibration points and thecalibration curve fit can produce less error for points along the curveoutside the calibration data points (interpolated or extrapolated). Thedistance between calibration points can actually be reduced to zero(i.e., 0% error at the calibration points) by using a plurality offunctions between the calibration points and the calibration curve.Together, the plurality of functions form a “piecewise continuousinterpolation” because they provide a calibrated value for thickness atall points within the calibration region. Additionally, certainfunctions can be chosen such that an extrapolation beyond thecalibration range is also accurate.

FIG. 9 illustrates application of continuous linear piecewiseinterpolation employing five calibration points 1, 2, 3, 4, 5, which areplotted based on the argument of impedance θ (or θ_(m) where thesubscript m indicates the measured argument of impedance) derived frommeasured eddy current sensor values at known conductive layerthicknesses t. The slope and intercept of the line between each of thepoints (i.e., between points 1 and 2, between points 2 and 3, betweenpoints 3 and 4, and between points 4 and 5) can be solved using atwo-equation, two-unknown matrix.

Upon using the calibrated eddy current sensor to measure the impedanceθ_(m) for a conductive layer having an unknown thickness, the portion ofthe continuous interpolation used is the portion on which the measuredimpedance θ_(m) falls. For example, if the measured impedance θ_(m) isθ_(a), then the point a falls between points 2 and 3, and Equation 16can used to determine the thickness t_(a) of the conductive layer.

$\begin{matrix}{t_{a} = {t_{2} + {\frac{\left( {t_{3} - t_{2}} \right)}{\left( {\theta_{3} - \theta_{2}} \right)} \cdot \left( {\theta_{a} - \theta_{2}} \right)}}} & {{Eq}.\mspace{14mu} 16}\end{matrix}$where t₂ is thickness at point 2, t₃ is thickness at point 3, θ₂ isimpedance at point 2, and θ₃ is impedance at point 3. It will beappreciated that if the point a fell between points 3 and 4, thenEquation 17 would be appropriate.

$\begin{matrix}{t_{a} = {t_{3} + {\frac{\left( {t_{4} - t_{3}} \right)}{\left( {\theta_{4} - \theta_{3}} \right)} \cdot \left( {\theta_{a} - \theta_{3}} \right)}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$where t₄ is thickness at point 4 and θ₄ is impedance at point 4. Theerror in measurement is a product of the distance between thecalibration points. Thus, for increased accuracy in a particular rangeof thicknesses (e.g., at low and/or high thicknesses), more calibrationwafers may be used.

If the measured impedance θ_(m) does not fall between two calibrationpoints, Equations 18 and 19 may be used to extrapolate based on thelowest calibration point (e.g., point 1 in FIG. 9) or the highestcalibration point (e.g., point 5 in FIG. 9).

$\begin{matrix}{\left. {\theta_{m} < \theta_{cal}^{\min}}\Rightarrow t_{m} \right. = {t_{cal}^{\min} - {\left( \frac{t_{cal}^{\min + 1} - t_{cal}^{\min}}{\theta_{cal}^{\min + 1} - \theta_{cal}^{\min}} \right) \cdot \left( {\theta_{cal}^{\min} - \theta_{m}} \right)}}} & {{Eq}.\mspace{14mu} 18} \\{\left. {\theta_{m} > \theta_{cal}^{\max}}\Rightarrow t_{m} \right. = {t_{cal}^{\max} + {\left( \frac{t_{cal}^{\max} - t_{cal}^{\max - 1}}{\theta_{cal}^{\max} - \theta_{cal}^{\max - 1}} \right) \cdot \left( {\theta_{m} - \theta_{cal}^{\max}} \right)}}} & {{Eq}.\mspace{14mu} 19}\end{matrix}$Applied to FIG. 9, θ_(cal) ^(min) is θ₁ (i.e., the impedance at point1), t_(cal) ^(min) is t₁ (i.e., the thickness at point 1), t_(cal)^(min+1) is t₂, θ_(cal) ^(min+1) is θ₂, θ_(cal) ^(maz) is θ₅ (i.e., theimpedance at point 5), t_(cal) ^(max) is t₅ (i.e., the thickness atpoint 5), t_(cal) ^(max−1) is t₄, and θ_(cal) ^(max−1) is θ₄. Inembodiments in which an impedance measurement on a known thickness ofzero (e.g., no calibration wafer or a calibration wafer free of aconductive layer), the linear piecewise continuous calibration curve isadvantageously accurate to about zero thickness without extrapolation.

FIG. 10A illustrates a linear piecewise continuous interpolationcalibration curve fit to the same set of calibration data, representedas circles, as described for FIGS. 5A-5E and 7. The calibration curvefits the actual data perfectly at each point (i.e., 0% error), and isaccurate between the calibration points and at extrapolations, as well.

Although the mathematics may be more complicated, functions other thanlines may also be used for each piecewise portion. For example,polynomials, trigonometric, hyperbolic, logarithmic, etc. functions maybe used among subsets of points. In some embodiments, the functions donot overlap (e.g., as illustrated for the linear piecewise continuousinterpolation of FIG. 10A), and as few as two functions may be createdin FIG. 9 (i.e., a first function using points 1, 2, 3; and a secondfunction using points 3, 4, 5).

FIG. 10B illustrates a second order polynomial piecewise continuousinterpolation calibration curve fit to the same set of calibration data,represented as circles. The calibration curves fit the actual dataperfectly at each point, and are accurate between the points and atextrapolations, as well.

FIG. 10C illustrates an overlapping second order polynomial piecewisecontinuous interpolation calibration curve fit to the same set ofcalibration data, represented as circles. In some embodiments, thefunctions at least partially overlap (e.g., with respect to FIG. 9, afirst function using points 1, 2, 3; a second function using points 2,3, 4; and a third function using points 3, 4, 5). In certain suchembodiments, the impedance θ_(a) of the point a would fall within eitherthe first function or the second function, and the user is presentedwith a plurality of options, including but not limited to: use only thet_(a) calculated from the first function (e.g., if θ_(a) is closer toθ₂); use only the t_(a) calculated from the second function (e.g., ifθ_(a) is closer to θ₂); use an average of t_(a) calculated from thefirst function and t_(a) calculated from the second function; use aweighted average of t_(a) calculated based on the distance of the pointa from the nearest calibration points; and use the t_(a) calculated fromthe function at which θ_(a) has the smaller slope. As illustrated inFIG. 10C, the overlapping portions are close enough to each other thatchoosing the incorrect function would not produce a large amount oferror.

The piecewise continuous interpolation therefore utilizes a searchalgorithm to find the appropriate function on which the measuredimpedance θ_(m) falls, and then plugs in the value of the measuredimpedance θ_(m) using that function to calculate the thickness t_(m) ofthe conductive layer. Those of skill in the art will appreciate thatmethods described herein may be incorporated into computer code (e.g.,into MATLAB® code) to automate determination of the values for thefunctions and use of the appropriate function to calculate thickness ofa conductive layer. Referring again to FIG. 2, the eddy current sensor214 may be in communication with the at least one controller 130, whichmay include a processor configured to execute a program that transformsa parameter measured by the eddy current sensor 214 (e.g., change inmagnetic flux density, argument of impedance θ) into a thickness of theconductive layer 205 in accordance with the continuous piecewiseinterpolation methods described herein.

FIG. 11 is a comparison of the amount of measurement error among fourcalibration techniques at thicknesses ranging from about 1.8 kÅ to about21 kÅ: smooth function interpolation wherein the function h_(j)(θ) issin h(j·θ); linear piecewise continuous interpolation; interpolationwherein the calibration curve is a fourth order polynomial (i.e.,c₁θ⁴+c₂θ³+c₃θ²+c₄θ+c₅ where c₁, c₂, c₃, c₄, and c₅ are coefficients),and smooth function interpolation wherein the function h_(j)(θ) is ln[sin h(j·θ)]. Although the illustrated error of the fourth orderpolynomial is about 8%, although this was a best case scenario, and theerror was generally at least 15% and even more than 20%. The hyperbolicsine and linear piecewise interpolations produce the least amount oferror, each having error of less than about 5% across the entirethickness range. In fact, the linear piecewise continuous interpolationachieves error of less than 2.6% and a standard deviation of abut 0.9%without any special adjustment in certain thickness regions (e.g.,adding more calibration wafers at low and high ends of the range).

The high accuracy of thickness measurements from the eddy currentsensors 214 by the smooth function interpolation and continuouspiecewise interpolation calibration methods described herein can makethe calibration of the sensors 214 robust to maintenance changes of theCMP apparatus 20 (e.g., changing the polishing pad 210, changing theplaten 208, etc.). Accordingly, the calibration does not need to berepeated after routine maintenance, which excepts hardware redesigns andchanges in the eddy current sensors. Eliminating calibration afterroutine maintenance can increase the productive time of the tool(“uptime”), thereby increasing throughput and reducing costs ofmanufacturing product workpieces. The uptime can be further extended dueto a reduction in calibration wafers used in the initial calibration, asdescribed above.

Endpoint and Transition Call Detection

With reference again to FIGS. 1 and 2, in certain embodiments, themonitored thickness of the conductive layer 205 may be used for endpointdetection and/or transition call detection in a polishing apparatus(e.g., the CMP apparatus 20). In endpoint detection for polishing, theapparatus is used to polish the conductive layer 205 of a workpiece 202until the conductive layer 205 is substantially removed (e.g., beingremoved from the field region between damascene structures). At thatpoint, the polishing process may be stopped, continued for a certainamount of time, etc. Previous eddy probe calibration techniques renderedthem unsuitable for endpoint detection because they were notsufficiently accurate at low thicknesses (for example as illustrated inFIGS. 5A-5E). As a result, the polishing was typically timed based onincoming conductive layer thickness and polishing rate, which could leadto over-polishing or under-polishing if the wafer had a differentincoming conductive layer thickness or polishing rate. However,calibration techniques in which the accuracy is less than 5% across arange of thicknesses that includes thicknesses below about 1 kÅ canprovide endpoint detection having accuracy down to about 200 to 500 Å.

In transition call detection for polishing, the apparatus is used topolish the bulk of the conductive layer 205 of a workpiece 202 with afirst process recipe, for example having an aggressive polishing rate,until the conductive layer 205 is very thin (e.g., to between about 3 kÅand 5 kÅ). At that point, the polishing process may be switched to asecond polishing recipe that polishes the remaining conductive layer,for example having a less aggressive polishing rate (e.g., until theremaining conductive layer is substantially removed). Previous eddyprobe calibration techniques rendered them unsuitable for transitioncall detection because they were not accurate at low thicknesses (forexample as illustrated in FIGS. 5A-5E). However, calibration techniquesin which the accuracy is less than 5% across a range of thicknesses thatincludes thicknesses below about 3.5 kÅ (e.g., to about 3 kÅ, 1 kÅ,etc.) can provide suitable endpoint detection, as the transition call isgenerally made at thicknesses less than about 3.5 kÅ.

Endpoint and transition call detection using accurately calibrated eddycurrent sensors can be extended to other processes as well, for exampleconductive layer plating. In endpoint detection for plating, theapparatus is used to plate the conductive layer 205 of a workpiece 202until the conductive layer 205 is at or proximate to a desiredthickness. At that point, the plating process may be stopped, continuedfor a certain amount of time, etc. In transition call detection forplating, the apparatus is used to plate the conductive layer 205 of aworkpiece 202 with a first process recipe, for example configured tofill small openings (e.g., damascene trenches or contact vias for wafermetallization), until the conductive layer 205 is at or proximate to adesired initial thickness. After reading the transition call, indicatinga thickness sufficient to fill the small openings, the remainder of theplating can be conducted with a second process recipe, for exampleconfigured to fill wide features without as much concern for bottom-upfilling.

Detection of the transition point allows process parameters (e.g.,pressure, temperature, current, slurry flow, oscillation/rotation speed,etc.) to be changed to efficiently remove or plate the conductive layer205, but to not over-polish or over-deposit the layer on the workpiece202, which may cause defects such as dishing or which may increase costsdue to longer process times, more material usage, or longer downstreamprocess times. In certain embodiments, the eddy current sensorcalibration utilized to monitor thickness can change after thetransition detection (e.g., to a more accurate calibration at low orhigh thicknesses).

In certain embodiments, the polishing station 200 includes an opticalsensor (not shown) that is configured to determine certain parameterssuch as the thickness of a conductive or non-conductive layer 205 on theworkpiece 202. For example, an optical sensor may simply detect a changein reflectivity or color of the workpiece (e.g., through a window in thepolishing pad 210) as the layer 205 is substantially removed. Such asensor can advantageously be used to supplement an eddy current sensor.For example, an endpoint may be determined when both an optical sensorand an eddy current sensor indicate that the thickness of the layer hasbeen reduced to a desired value. The optical sensor can also be used asa “check” against the eddy current sensor. However, as explained below,optical sensors alone may disadvantageously increase costs andcomplexity.

FIG. 12A illustrates experimental polish endpoint detection times foreleven wafers coated with a blanket layer of deposited copper. Theendpoint detection time is the time from beginning of a polishingprocess to the time when the thickness is proximate to a desired value(e.g., between about 200 and 500 Å). In the experiment depicted in FIG.12A, the endpoints were detected on each of the blanket wafers usingboth eddy current sensors calibrated as described herein and opticalsensors. FIG. 12A shows that the endpoint detection times using eddycurrent sensors (cross-hatched) are substantially similar to theendpoint detection times using optical sensors (solid), whichillustrates that properly calibrated eddy current sensors can be used toaccurately determine when to stop polishing a wafer at least asaccurately as an optical sensor.

FIG. 12B illustrates experimental polish endpoint detection times fornine patterned wafers having a layer of copper deposited thereon. Theendpoints were detected on each of the patterned wafers using both eddycurrent sensors calibrated as described herein and optical sensors. FIG.12B shows that, even on patterned wafers, the endpoint detection timesusing eddy current sensors (cross-hatched) are substantially similar tothe endpoint detection times using optical sensors (solid), whichillustrates that properly calibrated eddy current sensors can be used todetermine when to stop polishing a patterned wafer at least asaccurately as an optical sensor. The endpoint times in FIG. 12B arebimodal because the group clustered around 80 seconds detected anendpoint for 10 kÅ of copper over a standard feature pattern and thegroup clustered around 40 seconds detected an endpoint for 5.5 kÅ ofcopper over a different standard feature pattern. The endpoint detectionon the wafers having the standard feature pattern was more consistentusing the calibrated eddy current sensors (standard deviation of about0.8 seconds) than using the optical sensors (standard deviation of about2.1 seconds).

The accuracy of the calibrated eddy current sensors for endpointdetection advantageously allows an optical sensor to be omitted from CMPapparatuses. Eliminating the optical sensor can significantly reducecosts of the CMP apparatus, for example due to the expense of the sensorand related subsystems (e.g., polishing pads including a window for theoptical sensor to view the workpiece), and by reducing the complexity ofthe CMP apparatus (e.g., by reducing the number of wires coupled torotating parts).

FIGS. 13A and 13B illustrate experimental results for copper polishingof 1,000 wafers. Eddy current sensors calibrated with methods describedherein were used to determine the transition call from bulk polishingfrom a conductive layer thickness of about 12 kÅ to a thickness of about3 kÅ. FIG. 13B shows that the remaining copper after the transitiondetermination was consistent, with the wafer-to-wafer range being about377 Å. FIG. 13A shows that the amount of copper removed varied by about729 Å, which can be attributed to different incoming conductive layerthicknesses on different test wafers. Thus, regardless of the incomingthickness of the conductive layer, the calibrated eddy current sensorswere able to accurately measure thickness and stop the polishing processat a predetermined thickness. Such consistency is advantageous foruniformly further processing the wafers (e.g., by switching to a secondrecipe having a less aggressive polishing rate).

Continuous Closed Loop Control

As described above, the smooth function interpolation and continuouspiecewise interpolation eddy current sensor calibration methodsdescribed herein are accurate (e.g., within 5% error) over a large rangeof thickness values (e.g., at least between about less than 1 kÅ andabout 20 kÅ). Such accuracy allows closed loop control (“CLC”) ofpolishing and plating processes. In closed loop control, measuredthickness (by way of eddy current measurement of impedance) can be usedto adjust one or more process parameters during processing. For example,if the average thickness of the conductive layer 205 on a workpiece 202being polished is too high, the CLC system can increase the rate ofrelative motion between the workpiece 202 (and/or subsequent workpieces)and the polishing pad 210 (e.g., by increasing the orbital or rotationalspeed of the workpiece carrier 206). Changing a wide variety of processparameters are possible, including but not limited to, a process recipe,an on/off state, pressure, temperature, fluid (e.g., slurry) flow,movement (e.g., oscillation or rotation) speed, and current.

In some embodiments, each sensor 300 a, 300 b, 300 c, 300 d (FIGS. 3Aand 3B) corresponds to a processing zone in which one or more parametersmay be changed based on the thickness measurement. The shape of thezones may correspond to the movement between the workpiece 202 and thesensors 300 a, 300 b, 300 c, 300 d (e.g., arcuate, annular, linear,etc.). As an example, in the workpiece carrier 206 (FIG. 2), the bladdermay have corresponding zones such that head pressure can be changed foronly part of a workpiece being processed. Thus, if the sensor 300 bdetermines that a thickness is too high relative to the thicknessdetermined by the sensors 300 a, 300 c, 300 d, the head pressure in thezone corresponding to the sensor 300 b may be increased such that theportions of the workpiece 202 in that zone have more contact with thepolishing pad 210, thereby increasing the polishing rate. As will beappreciated by the skilled artisan in view of the present disclosure,examples of parameters that can be changed differently in differentzones includes, but is not limited to, pressure, temperature, fluid(e.g., slurry) flow, movement (e.g., oscillation or rotation) speed, andcurrent.

FIG. 14 illustrates an experimental plot of the polishing of aconductive layer from two wafers. Both wafers started with a conductivelayer having a thickness of about 16 kÅ and were polished to a targetthickness of about 3 kÅ. The first wafer (open circles) was polishedwithout using CLC (i.e., the process parameters were constant throughoutthe polishing process). The incoming profile was not preserved (i.e.,the thickness on the edges became much lower than the thickness overmost of the rest of the wafer), and the 1-sigma variation was about 457Å (3.57%). The second wafer (solid diamonds) was polished using CLC forsix zones in which the pressure was changed in each zone based on amonitored thickness. The incoming profile was advantageously preserved(i.e., the thickness difference on the edges of the wafer more closelymatched the thickness difference on the edges of the incoming wafer),and the 1-sigma variation was about 275 Å (2.15%). Thus, the secondwafer polished using CLC had better uniformity and was better able tomaintain a desired within-wafer thickness profile.

It will be appreciated that the methods described herein are not limitedto any particular process or tool, but may be used for any tool orprocess in which knowledge of the thickness of a conductive layer may beuseful. Examples of suitable tools are the XCEDA™ CMP tool and SABRE®Electrofill™ tool, both available from Novellus Systems, Inc. of SanJose, Calif. The eddy current sensor calibration methods describedherein may also be used as a general mathematical platform to calibratesystems for which calibration over a broad range of conductive layerthicknesses is desired. For example, eddy current sensors can be used todetermine the thickness of conductive layers prior to or afterconductive layer processes, in situ and/or ex situ.

Although this invention has been disclosed in the context of certainpreferred embodiments and examples, it will be understood by thoseskilled in the art that the present invention extends beyond thespecifically disclosed embodiments to other alternative embodimentsand/or uses of the invention and obvious modifications and equivalentsthereof. In addition, while several variations of the invention havebeen shown and described in detail, other modifications, which arewithin the scope of this invention, will be readily apparent to those ofskill in the art based upon this disclosure. It is also contemplatedthat various combinations or sub-combinations of the specific featuresand aspects of the embodiments may be made and still fall within thescope of the invention. It should be understood that various featuresand aspects of the disclosed embodiments can be combined with, orsubstituted for, one another in order to form varying modes of thedisclosed invention. Thus, it is intended that the scope of the presentinvention herein disclosed should not be limited by the particulardisclosed embodiments described above, but should be determined only bya fair reading of the claims that follow.

What is claimed is:
 1. A method of processing a wafer, the methodcomprising: changing the thickness of a conductive layer on the wafer;and during changing, monitoring the thickness of the conductive layer,wherein monitoring the thickness comprises correlating a measurementfrom an eddy current sensor to a thickness of the conductive layer,wherein correlating the measurement to the thickness comprises applyinga model that includes either (1) a plurality of functions betweenmeasurement points of known thicknesses or (2) an analytic functionhaving infinite order terms.
 2. The method of claim 1, wherein changingcomprises polishing the conductive layer.
 3. The method of claim 1,wherein changing comprises plating the conductive layer.
 4. The methodof claim 1, wherein the measurement comprises a magnetic flux densitychange in a magnetic field.
 5. The method of claim 4, whereincorrelating the measurement to the thickness comprises calculating anargument of impedance.
 6. The method of claim 1, wherein applying themodel is accurate to within 5% error over a range from about 1 kÅ toabout 20 kÅ.
 7. The method of claim 1, wherein the analytic functioncomprises hyperbolic sine (sin h).
 8. The method of claim 1, furthercomprising: indicating a transition point when a monitored thickness isproximate to a predetermined value; and continuing to change thethickness of the conductive layer after indicating the transition point.9. The method of claim 1, further comprising indicating an endpoint whena monitored thickness is proximate to a predetermined value.
 10. Themethod of claim 9, wherein the predetermined value is less than about500 Å.
 11. The method of claim 1, further comprising adjusting a toolparameter by using the monitored thickness.
 12. The method of claim 11,wherein adjusting the tool parameter comprises closed loop control. 13.The method of claim 1, wherein monitoring the thickness comprises usinga plurality of eddy current sensors to separately monitor thethicknesses of the conductive layer in a plurality of different zones.14. The method of claim 13, further comprising adjusting a toolparameter in one of said zones separately from others of said zonesusing the monitored thicknesses.
 15. A method of processing a wafer, themethod comprising: changing the thickness of a conductive layer on thewafer; and during changing, monitoring the thickness of the conductivelayer, wherein monitoring the thickness comprises correlating ameasurement from an eddy current sensor to a thickness of the conductivelayer, wherein correlating the measurement to the thickness comprisesapplying a model that includes a plurality of functions betweenmeasurement points of known thicknesses.
 16. The method of claim 15,wherein changing comprises polishing the conductive layer.
 17. Themethod of claim 15, wherein changing comprises plating the conductivelayer.
 18. The method of claim 15, wherein the measurement comprises amagnetic flux density change in a magnetic field.
 19. The method ofclaim 18, wherein correlating the measurement to the thickness comprisescalculating an argument of impedance.
 20. The method of claim 15,wherein applying the model is accurate to within 5% error over a rangefrom about 1 kÅ to about 20 kÅ.
 21. The method of claim 15, furthercomprising: indicating a transition point when a monitored thickness isproximate to a predetermined value; and continuing to change thethickness of the conductive layer after indicating the transition point.22. The method of claim 15, further comprising indicating an endpointwhen a monitored thickness is proximate to a predetermined value. 23.The method of claim 22, wherein the predetermined value is less thanabout 500 Å.
 24. The method of claim 15, further comprising adjusting atool parameter by using the monitored thickness.
 25. The method of claim24, wherein adjusting the tool parameter comprises closed loop control.26. The method of claim 15, wherein monitoring the thickness comprisesusing a plurality of eddy current sensors to separately monitor thethicknesses of the conductive layer in a plurality of different zones.27. The method of claim 26, further comprising adjusting a toolparameter in one of said zones separately from others of said zonesusing the monitored thicknesses.